2. Suppose we are given the following information about a signal x(t):i. x(t) is real and odd.ii. x(t) is periodic with period T = 2 and has Fourier coefficients ak.iii. ak = 0 for Ikl >I.iv. H6laco)F dt = 1.Specify two different signals that satisfy these conditions

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Answered: 2. Suppose we are given the following…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1B.) Find the period, the amplitude and the phase shift (if any).
Consider a function a(t) with a period T, = 3 and Coz = 5 Given another function: y(t) = -2x(t+ 2) + 1 Find the Fourier coefficient Cy in terms of the Fourier coefficient C: Select one: O Cry = Crek8a/3 O Cy = Cjk4n/3 O Cky Chze jkAn/3 O Cky
Suppose that f(t) is periodic with period [-n, n) and has the following complex Fourier coefficients: Co = -3, 1 = -3+3i, C2 = 3, C3 = -4 + 2i, ... ... (A) Compute the following complex Fourier coefficients. C3 = (B) Compute the real Fourier coefficients. (Remember that et kt = cos(kt) + i sin(kt).) %3| ao = > a2 = > az = bi bz = %3D (C) Compute the complex Fourier coefficients of the following. (1) The derivative f (t). Co (ii) The shifted function f(t +) Co C2 Ca= (iii) The function f(3t). Co C1 = %3D
2) Derive an expression for the x(t) and Determine the Fourier transform of the signal x(t) shown in Figure 2. x(t) cos at Şekil 2
please label the question and answer clearly. also please answer part D and E. thank you!!!
6) Find Fourier transform of: 1) 90 88 e-n(y² +y)(x-y)e-lx-yldy f 2) -πy² nye dy
2. Determine the complex Fourier coefficients co and c„ of the function simulating the periodic heating of a room if it is given that f(t) = e' – 1, 0
Suppose that f(t) is periodic with period [-T, 7) and has the following complex Fourier coefficients: -4, C1 —3+ 41, С2 —D —1- 21, C3 2. (A) Compute the following complex Fourier coefficients. C_3 = 2 C_2 =-1+2i C_1 = (B) Compute the real Fourier coefficients. (Remember that ei kt cos(kt) + i sin(kt).) ao = a1 = -6 , a2 = -2 , az = 4 b, = b2 = b3 = (C) Compute the complex Fourier coefficients of the following. (i) The derivative f' (t). Co = C1 = -4-31 C2 = C3 = (ii) The shifted function f(t + Co = C = C2 = C3 = (iii) The function f(3t). Co = C = C2 = C3 =
Determine the Fourier transform of a signal with g(t) = At/B between t = 0 and t = B and g(t) = 0 elsewhere. Then find the Fourier transform of the following signal, which is a special case of the g(t): f(t) 1 0 1 t
The Fourier series coefficients for the signal shown are:
9
4. The table shows the number C of cars in an office parking lot over the course of a work day. The time t is measured in hours, with t 0 representing 7:00am. 10 11 12 0. 1 3 6. 7 75 100 110 86 34 12 C 13 67 92 108 82 52 15 a) You want to write a sinusoidal model for the data in the table without using a graphing calculator. Is it more convenient to model the data with a sine or cosine function? Explain. b) Write a sinusoidal model for the number C of cars as a function of the time t (in hours) without using a graphing calculator. Identify and explain how you calculated your values for the amplitude, period, horizontal shift, and vertical shift. c) Use a graphing calculator to write a sinusoidal model that gives C as a function of t. d) Using your model from part (c), at about what time(s) will there be 45 cars in the parking lot? Revised May 2016 Page 4

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2. Suppose we are given the following information about a signal x(t): i. x(t) is real and odd. ii. x(t) is periodic with period T = 2 and has Fourier coefficients ak. iii. ak = 0 for Ikl >I. iv. lao)F dr = 1. Specify two different signals that satisfy these conditions